Answer :
David wants to buy a boat worth \[tex]$30,000 when he retires in 20 years. He currently has \$[/tex]12,000 in his simple interest savings account. Let's evaluate his options to determine the best course of action for him to reach his financial goal.
### Option 1: Keep his money where it is and be patient
If David keeps his \[tex]$12,000 in a simple interest account, he will earn interest at a constant rate every year. The formula for simple interest is: \[ \text{Simple Interest} = P \times r \times t \] where \(P\) is the principal amount, \(r\) is the annual interest rate, and \(t\) is the time in years. However, simple interest typically grows at a slower rate compared to other investment options, and it is likely insufficient for him to reach \$[/tex]30,000 with the initial amount he has.
### Option 2: Move his money to an IRA or Certificate of Deposit (CD)
IRAs (Individual Retirement Accounts) and Certificates of Deposit generally offer more favorable interest rates than a regular savings account but often come with penalties for early withdrawal and fixed terms. Although these accounts may help his savings grow, inflexibility and penalties may not be the optimal choice for maximizing his returns efficiently within his specific timeline.
### Option 3: Move his money to a compound interest account
Compound interest accounts capitalize on the effect of compounding, where interest is earned on both the initial principal and the interest that has already been added to the account. This can significantly increase his savings over time. The formula for compound interest is:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where [tex]\(A\)[/tex] is the amount of money accumulated after [tex]\(n\)[/tex] years, including interest, [tex]\(P\)[/tex] is the principal amount (the initial sum of money), [tex]\(r\)[/tex] is the annual interest rate, [tex]\(t\)[/tex] is the time in years, and [tex]\(n\)[/tex] is the number of times that interest is compounded per year. Because compound interest can result in exponential growth over a long period, it is often the most efficient way to grow savings.
### Option 4: Move his money to a business checking account
Business checking accounts generally do not offer interest, or if they do, the interest rate is very low. They are designed for handling large transactions and managing business finances efficiently rather than growing savings. Therefore, this is not a suitable option for David’s goal of maximizing his savings.
### Conclusion
To reach his goal of \$30,000 by retirement in 20 years, David should move his money to a compound interest account. This option provides the highest potential for growth due to the compounding effect, which will enable him to accumulate the necessary funds to purchase his boat.
Therefore, the best course of action for David is:
[tex]\[ \boxed{3\ \text{Move his money to a compound interest account}} \][/tex]
### Option 1: Keep his money where it is and be patient
If David keeps his \[tex]$12,000 in a simple interest account, he will earn interest at a constant rate every year. The formula for simple interest is: \[ \text{Simple Interest} = P \times r \times t \] where \(P\) is the principal amount, \(r\) is the annual interest rate, and \(t\) is the time in years. However, simple interest typically grows at a slower rate compared to other investment options, and it is likely insufficient for him to reach \$[/tex]30,000 with the initial amount he has.
### Option 2: Move his money to an IRA or Certificate of Deposit (CD)
IRAs (Individual Retirement Accounts) and Certificates of Deposit generally offer more favorable interest rates than a regular savings account but often come with penalties for early withdrawal and fixed terms. Although these accounts may help his savings grow, inflexibility and penalties may not be the optimal choice for maximizing his returns efficiently within his specific timeline.
### Option 3: Move his money to a compound interest account
Compound interest accounts capitalize on the effect of compounding, where interest is earned on both the initial principal and the interest that has already been added to the account. This can significantly increase his savings over time. The formula for compound interest is:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where [tex]\(A\)[/tex] is the amount of money accumulated after [tex]\(n\)[/tex] years, including interest, [tex]\(P\)[/tex] is the principal amount (the initial sum of money), [tex]\(r\)[/tex] is the annual interest rate, [tex]\(t\)[/tex] is the time in years, and [tex]\(n\)[/tex] is the number of times that interest is compounded per year. Because compound interest can result in exponential growth over a long period, it is often the most efficient way to grow savings.
### Option 4: Move his money to a business checking account
Business checking accounts generally do not offer interest, or if they do, the interest rate is very low. They are designed for handling large transactions and managing business finances efficiently rather than growing savings. Therefore, this is not a suitable option for David’s goal of maximizing his savings.
### Conclusion
To reach his goal of \$30,000 by retirement in 20 years, David should move his money to a compound interest account. This option provides the highest potential for growth due to the compounding effect, which will enable him to accumulate the necessary funds to purchase his boat.
Therefore, the best course of action for David is:
[tex]\[ \boxed{3\ \text{Move his money to a compound interest account}} \][/tex]
